Abner is engaged to actress Hallie Foote and appeared in Alone alongside Foote. His father-in-law, Horton Foote, wrote the stage play "The Trip to Bountiful" in which Abner portrayed the role of Ludie Watts in 2003 and between 2005 and 2006. In 2006 he received a Drama Desk Award nomination for best featured actor for his performance in this play.